Linear and quadratic models of the southern Murray-Darling basin

Linear programming (LP), a well-established technique for modelling agricul tural and other systems, has been extensively used to model irrigation syst ems in Australia. The models constructed have been used to assess the effec ts of changing water charges on farm incomes, water use, and the effects of trade in water allocations. An LP model that reflects actual farm behaviou r requires a large amount of data. Moreover, demand and supply functions es timated with LP models are necessarily stepped rather than smooth. Howitt h as suggested a way of escaping from these problems of LP models. His positi ve programming approach replaces an LP model with a simpler quadratic progr amming model. In this paper, Howitt's approach is used to develop a quadrat ic programming model from an existing LP model of irrigated agriculture in the southern Murray-Darling basin of Australia. A comparison of the quadrat ic and linear models indicates that the quadratic programming model is smal ler and simpler to specify and that it produces similar results to the line ar model, in terms of cropping, trade, and demand for irrigation water. The choice of modelling technique depends on the problem and the available res ources. Positive programming can be a valuable addition to the farm modelle rs' arsenal. (C) 2001 Elsevier Science Ltd. All rights reserved.